SUMMARY

Small terrestrial animals continually encounter sloped substrates when
moving about their habitat; therefore, it is important to understand the
mechanics and kinematics of locomotion on non-horizontal substrates as well as
on level terrain. To this end, we trained gray short-tailed opossums
(Monodelphis domestica) to move along level, 30° inclined, and
30° declined trackways instrumented with a force platform. Vertical,
craniocaudal and mediolateral impulses, peak vertical forces, and required
coefficient of friction (μreq) of individual limbs were
calculated. Two high speed video cameras were used to simultaneously capture
whole limb craniocaudal and mediolateral angles at limb touchdown, midstance
and lift-off. Patterns on the level terrain were typical for non-primate
quadrupeds: the forelimbs supported the majority of the body weight, forelimbs
were net braking and hindlimbs net propulsive, and both limb pairs exerted
small laterally directed impulses. M. domestica moved more slowly on
sloped substrates in comparison to level locomotion, and exhibited a greaterμ
req. On inclines, both limb pairs were more protracted at
touchdown and more retracted at lift-off, fore- and hindlimbs had equal roles
in body weight support, forelimbs exerted greater propulsive impulse than
hindlimbs, and μreq was greater in the forelimbs than in
hindlimbs. On declines, only the forelimbs were more protracted at touchdown;
forelimbs supported the great majority of body weight while they generated
nearly all of the braking impulse and, despite the disparity in fore-
vs hindlimb function on the decline, μreq was not
significantly different between limbs. These differences on the inclined and
declined surfaces most likely result from (1) the location of the opossums'
center of mass, which is closer to the forelimbs than to the hindlimbs, and
(2) the greater functional range of the forelimbs versus the
hindlimbs.

Introduction

The natural habitats of most small mammals are replete with heterogeneous
substrates, including sloped terrain, rocks, and fallen and growing
vegetation, so that small mammals must frequently move over or around sloped
substrates. In order to fully understand how small mammals utilize their
habitats and the mechanics of movement in these habitats, it is necessary to
examine locomotor biomechanics on a variety of substrates. Yet, until
recently, data on the biomechanics of animal locomotion were usually gathered
from the rarest of natural substrates: flat, horizontal, straight trackways.
Such data are valuable as they provide a baseline condition to which
locomotion along a graded or irregular substrate may be compared. Although
differences among clades of mammals have been reported (e.g.
Jayes and Alexander, 1978;
Demes et al., 1994;
Schmitt and Lemelin, 2002),
the substrate reaction forces (SRFs, a measure of overall limb function) of
most quadrupedal mammals moving linearly along a flat and level trackway using
a symmetrical gait follow a common pattern. The vertical component of the SRF
is by far the largest in magnitude because of its role in body weight support.
Forelimb vertical SRFs tend to exceed those of hindlimbs because the center of
mass of most mammals is located closer to the forelimbs than to the hindlimbs.
The craniocaudal (longitudinal or fore–aft) SRF is characterized by an
initial braking component followed by a propulsive component; the braking
component is typically larger than the propulsive component in the forelimbs
whereas the hindlimbs are usually net propulsive. Mediolateral (transverse)
forces tend to be relatively small and, at least for cursorial mammals, they
show no strong pattern of direction.

Support of body weight, forward propulsion and stability are maintained
during terrestrial locomotion (both level and graded substrates) in large part
by adjusting limb function and locomotor posture, including the degree of limb
excursion. The inescapable effects of gravity necessitate shifts in limb
function (as reflected by SRFs) when moving on graded substrates. The few
studies that have reported SRFs on graded surfaces focused either on bipeds
(Dial, 2003;
Dick and Cavanagh, 1987;
Gottschall and Kram, 2005) or
highly derived tetrapods such as horses
(Dutto et al., 2004). Based on
these studies and on general principles of mechanics, we formulate several
predictions for how a generalized mammal might adjust limb function when
moving along a grade.

Uphill locomotion is expected to unload the forelimb somewhat while
downhill locomotion should increase the forelimb's load. If this prediction is
borne out, then on the incline the vertical impulse and peak vertical force
will decrease in the forelimb (relative to the vertical impulse and peak
vertical force generated by the forelimb on the level trackway). Vertical
impulse and peak force should increase in the hindlimb, relative to the level
trackway trials. On the decline, this pattern should be reversed.

Both limb pairs must generate additional propulsive effort to raise the
center of mass uphill, whereas a greater braking effort is required when
moving downhill to counter the acceleration due to gravity. It is obvious that
more propulsive effort will be required on the incline (and more braking
effort on the decline). But what is not known is the degree to which braking
impulse will be reduced in the incline, and propulsive force on the decline.
Kinetic studies of horses walking up 10% inclines show that braking forces are
reduced, but not eliminated, when moving up-slope. Propulsive forces are
increased (Dutto et al.,
2004). In this study, the animals moved on 30° slopes.
Relative to Dutto et al. we expect a greater reduction in braking forces on
the incline (Dutto et al.,
2004), and a similar reduction in propulsive forces on the
decline.

The required coefficient of friction [μreq, the ratio of
shear force to normal force (Redfern et
al., 2001)] will be greater on sloped trackways than on the level
trackway because shear forces should increase as a result of the gravitational
force, while the normal force component of the animal's weight will decrease.
In order to avoid slipping on a substrate, an animal must generate sufficient
friction force by either increasing the normal force (perpendicular to the
substrate) and/or decreasing the shear force (parallel to the substrate).
Either or both of these adjustments effectively reduce the μreq
and thereby decrease the likelihood of slipping. Although we expect that the
vertical force will vary between limb pairs on the inclines and declines, we
do not expect that the body weight support roles of the forelimbs and
hindlimbs to affect the μreq. The reason for this is that normal
and shear force components of the vertical force will naturally increase (or
decrease) in proportion to the vertical force. However, if the braking and
propulsive roles of a limb pair change substantially, then the corresponding
increase or decrease in shear forces will cause an increase or decrease inμ
req.

The mediolateral SRFs will not differ significantly among slopes because
there is no change in the gravitational force in the mediolateral direction in
these experiments. Furthermore, it seems unlikely that a 30° slope will
sufficiently destabilize the animal in a mediolateral axis to cause the
mediolateral forces to differ among substrates.

The limbs will adopt a more crouched posture on the sloped trackways,
bringing the shoulder and hip joints closer to the substrate. This kinematic
adjustment will make the animal more stable because the line of gravity
passing through the animal's center of mass (G) will remain closer to
the center of the base of support generated by the supporting limbs.
Furthermore, animals climbing slopes and/or arboreal substrates might also be
predicted to shorten their effective limb lengths in order to decrease the
likelihood that the body will topple backward (in the case of uphill
locomotion) or forward (in the case of downhill locomotion). This prediction
is borne out in cats moving on inclined trackways
(Carlson-Kuhta et al.,
1998).

To test these predictions of how SRFs and general limb kinematics change on
sloped versus horizontal trackways in a generalized mammal, we ran
gray short-tailed opossums Monodelphis domestica Wagner 1842 on
level, 30° inclined, and 30° declined trackways. M. domestica
is a small, terrestrial marsupial that retains many primitive morphological
traits (Lee and Cockburn,
1985; Novacek,
1992), and so it is likely that these findings may yield insight
into how primitive mammals might have been constrained to move on inclines and
declines. When these data are compared to records of mammals which have
evolved novel features, hypotheses about the evolution of locomotor mechanics
among mammals can be generated.

Materials and methods

Animals

All animal care and experimental procedures followed Ohio University
Institutional Animal Care and Use Committee approved guidelines. Locomotor
biodynamics were assessed on a level trackway in six gray short-tailed
opossums Monodelphis domestica Wagner 1842, 89–150 g) and on
angled trackways with a separate set of five opossums (80–103 g). Prior
to data collection, the opossums were trained to run on the trackways so that
they would be accustomed to the apparatus and run steadily in a straight line.
The carcasses of three additional M. domestica of comparable size
(77–93 g) were used to calculate the craniocaudal location of the center
of mass (COM) using the reaction board method
(Özkaya and Nordin,
1999). Briefly, the animal was positioned on a platform with a
knife-edge at each end (Fig.
1); we constructed this platform by driving three nails through a
piece of foamcore 40 cm long. One edge of the platform was placed on a digital
scale, and the other end was placed upon a block so that the platform was
level. The distance between the knife edges (l) was measured, and the
weight of the platform (Wp) was obtained. The specimen was
placed upon the platform so that its caudal end reached the knife edge of the
platform opposite of the scale, and the digital scale measured the amount of
weight supported by the knife edge over the scale (Rs).
Using the actual weight of the specimen (Ws), the
following equation was used to calculated the craniocaudal location of the
center of mass:
where Ycom is the distance between the knife edge over the
support block and the animal's center of mass.

Measurement of the craniocaudal center of mass. The dead animal was placed
on its side, with the limbs arranged in a manner that resembled a standing
position. The tail was positioned at about a 45° angle in the sagittal
plane relative to the long axis of the body; this is approximately the same
tail posture that is adopted during normal movement. l, length of
platform between knife points; Ycom, distance between
knife point and center of mass; Ws, weight of opossum;
Wp, weight of knife point platform. See text for
formula.

Force data acquisition

Two terrestrial trackways were constructed, a level trackway (160 cm long,
11 cm wide) and a 30° sloped trackway (180 cm long, 11 cm wide). The
sloped trackway was stabilized through the use of extensive buttressing and
base weighting so that mechanical vibrations from the base were not introduced
to the force transducers. A force platform (48 cm long, 11 cm wide for the
level trackway, and 36 cm long, 11 cm wide for the sloped trackway) was
installed flush and parallel to the surface of each trackway
(Fig. 2A). The force platform
was equivalent to the strain gage-based, spring-blade design described
elsewhere (Parchman et al.,
2003). Analog outputs from the force platforms captured at 1200 Hz
(level trials) and 500 Hz (sloped trials) for 3–6 s were amplified (SCXI
1000 and 1121, National Instruments, Austin, TX, USA), converted from analog
to digital (NB-M10-16L, National Instruments), and recorded using LabVIEW
(National Instruments) virtual instruments. The raw voltages were then
converted into three-dimensional substrate reaction forces (SRFs) oriented
relative to the surface of the platform (and the opossum's body): dorsoventral
(FDV), craniocaudal (FCC) and mediolateral
(FML). These forces were filtered using a Butterworth notch
filter (between 51–61 Hz for FDV and
FCC; between 93–103 Hz for FML)
prior to analysis. Individual limb SRFs were obtained as the first footfall
(forelimb) and last footfall (hindlimb) on the platform surface. Trials used
to obtain fore- and hindlimb data did not differ significantly in speed.

(A) Data collection setup, illustrating how forelimb force data were
collected (first contact with force platform). In this diagram, the opossum is
moving up the incline, and a single forelimb has stepped onto the force plate.
(B,C) Digitized landmarks and the calculation of overall limb excursion
angles. Protraction angle was measured at touchdown, retraction angle was
measured at lift-off, and mediolateral angles were measured at both
events.

Only trials in which the opossum moved at a near steady speed were
evaluated further. This was determined either by calculating forward speed at
four intervals from the overhead videos or (for the level trackway only) by
integrating the whole body craniocaudal acceleration over the entire force
plate to estimate forward speed (Parchman
et al., 2003). If the speed over any part of the trial was 15%
above or below step speed, the trial was discarded. In spite of great effort
to obtain equivalent forward speeds on the level and sloped runways, the
opossums moved significantly faster on the level trackway (1.51±0.05 m
s–1) than on the sloped trackways (incline, 0.87±0.03
m s–1; decline, 0.84±0.03 m s–1;
P<0.0001; no significant difference in speed between incline and
decline trials). Previous studies in other species also found that preferred
speed decreases on non-level substrates
(Wickler et al., 2000).

The role of limbs in body weight support was assessed using vertical force
(FV, computed as the vector sum of the vertical components
of FDV and FCC) and vertical impulse
(calculated by integrating FV through time). The function of
limbs in controlling forward motion was determined by the magnitude of braking
(negative) and propulsive (positive) components of the craniocaudal impulse.
The net mediolateral impulse (sum of medial and lateral impulses) reflected
overall limb function in maintaining lateral stability. In addition, time to
peak FV and time to FCC=0 (when the
FCC profile switches from braking to propulsive) were
measured relative to support duration. The required coefficient of friction
(μreq) was calculated as the ratio of shear force (vector sum of
FCC and FML) to normal force
(FDV) (Redfern et al.,
2001). Although μreq was determined over the entire
stance phase, only median values were evaluated; the median was used rather
than the mean because the median would be influenced less by the relatively
large μreq at touchdown and lift-off.

Images from the cameras were uploaded using VideoStudio 4.0 (U-lead,
Taipei, Taiwan) and three-dimensional coordinates for all landmarks were
determined using APAS (Ariel Dynamics, San Diego, CA, USA). The timing of
forelimb and hindlimb touchdown and lift-off was determined from the videos.
The footfall timing data were used to calculate stride duration (time between
two footfalls of the same hindlimb), duty factor (percentage of stride
duration where the reference hindlimb was in contact with the substrate), and
limb phase [percentage of the stride when the ipsilateral forelimb contacted
the substrate after the reference hindlimb
(Hildebrand, 1976)]. The
three-dimensional coordinates were used to calculate angular data for the
fore- and hindlimb (Fig. 2B,C).
The craniocaudal angle of the whole limb was measured for each limb pair at
touchdown, midstance and lift-off. For the forelimb, these angles were
calculated from the coordinates of the shoulder, tip of the third manual
digit, and a point projected directly posterior to the shoulder joint
(parallel to the substrate surface). In the hindlimb, these craniocaudal
angles were calculated from the hip, metatarsophalangeal joint, and a point
projected directly posterior to the hip joint (parallel to the substrate
surface). Mediolateral angles at touchdown, midstance and lift-off were
calculated for fore- and hindlimbs; the purpose of this measurement is to help
explain differences in mediolateral impulses (if any) among substrates and
between limb pairs. Mediolateral angles were calculated by projecting a point
lateral to the shoulder or hip markers (parallel to the trackway surface),
respectively. Shoulder and hip heights perpendicular to the trackway surface
were measured at touchdown, midstance and lift-off. These were calculated by
measuring the perpendicular distance between the shoulder and substrate and
between the hip and substrate, respectively.

Statistics

Force data were adjusted for body weight to account for difference in body
size across the sample. Data from all individuals were pooled, and the Systat
9.0 (Point Richmond, CA, USA) statistical package was used for all analyses.
We used least-squares linear regression to determine if a relationship existed
between speed and each kinematic and kinetic variable (shoulder and hip
heights at touchdown, midstance and lift-off; craniocaudal and mediolateral
angles at touchdown, midstance and lift-off; peak vertical force; vertical,
braking, and propulsive impulses; and net mediolateral impulse). When
significant correlations existed, we used two-way analysis of covariance
(ANCOVA) to make comparisons among slopes (level, incline and decline) and
between limb pairs (forelimb, hindlimb). There was no speed effect among most
variables, however, and in these situations two-way fixed-factor ANOVA was
used. Because different animals were used for level and non-level trials, we
did not use repeated-measures ANOVA. When significant interaction between
slope and limb groups was detected, we tested each factor (slope, limb)
separately. The sequential Bonferroni technique
(Rice, 1989) was used to
determine significance level (α=0.05). When significant differences
among substrates were found, a Bonferroni post-hoc test was used to
determine which substrates were significantly different from each other.

Results

The center of mass of M. domestica was determined to lie
37.0±1.8% (N=3, mean ± s.e.m.) of the distance between
the glenohumeral and hip joints (i.e. closer to the glenohumeral joint).

Kinematics

The animals moved significantly faster on the level trackway
(1.511±0.051 m s–1) than on the sloped trackways
(incline, 0.874±0.027 m s–1; decline,
0.835±0.029 m s–1; P<0.0001). There was no
significant difference in speed between incline and decline trials.
Furthermore, trials used to obtain fore- and hindlimb data on each trackway
type did not differ significantly in speed. Incline trials had the highest
duty factor (39.9±1.3%), followed by declines (34.4±1.0%) and
then level (30.2±0.9%; P≤0.012;
Fig. 2); duty factor never
exceeded 50% on any slope. Gait, determined by limb phase, was also affected
by substrate slope (P≤0.001): limb phase was significantly lower
on decline trials (38.7±1.2%) than on the incline (46.8±1.6%) or
level trials (51.1±1.1%; P≤0.001; no significant difference
between incline and level). Therefore, the opossums kinematically trotted
during the level and incline trials whereas the decline trials are primarily
lateral-sequence diagonal-couplets, a four-beat, trot-like gait
(Fig. 3).

Shoulder and hip height data are summarized in
Table 1. Hip height was always
greater than shoulder height (P<0.0001) on all substrates. During
stance phase, shoulder height was lower at touchdown and midstance on the
incline in comparison to the level and decline (P=0.0196; no
significant difference in shoulder height between decline and level
substrates). By comparison, hip height was always significantly lower on the
decline substrates than on incline or level substrates (P=0.0195; no
significant differences in hip height between incline and level substrates).
Shoulder and hip heights (relative to the trackway surface) changed cyclically
on all trackway orientations, so that shoulders and hips reached their lowest
position at midstance.

Angular data are summarized in Table
1 and significant differences between slope groups are illustrated
in Fig. 4. Fore- and hindlimbs
were significantly more protracted at touchdown on all sloped trials than they
were on the horizontal trackway (P=0.0001); there was no significant
difference in degree of protraction at touchdown between incline and decline
trials. At midstance, both fore- and hindlimbs were retracted, regardless of
substrate, but the amount of retraction decreased from level → incline→
decline (P≤0.0041). Both limb pairs were significantly less
retracted at lift-off on the declined trackway than on the level and inclined
trackways (P=0.0001). Craniocaudal angles at touchdown, midstance and
lift-off were not correlated with speed, with the exception of the hindlimb
retraction angle at lift-off on the downslope (least-squares regression,
P=0.0035, r2=0.483, i.e. a weak tendency to
undergo greater retraction at higher speeds). Mediolateral angle of each limb
at touchdown, midstance and lift-off did not vary across substrates. However,
mediolateral angle at touchdown was significantly lower in hindlimbs compared
to forelimbs (P<0.0001).

Schematic of sagittal plane parameters for the forelimbs (above) and
hindlimbs (below) of M. domestica on level, incline and decline
trackways (left to right). Fore- and hindlimb touchdown (solid gray bar) and
lift-off (open bar) angles are exaggerated to make differences between limbs
and substrates more visible. Vertical impulse is represented by broken arrows,
and braking and propulsive impulses by solid arrows; the magnitudes of these
impulse vectors are also not shown to scale with each other for illustrative
effect (see Table 1 for exact
values). B, braking impulse; P, propulsive impulse.

Kinetics

Sample force profiles are shown in Fig.
5. Few speed-dependent relationships were found among the kinetic
parameters. While significant correlations were determined for peak vertical
force in forelimbs on declines and hindlimbs on all substrates
(Table 2), only a single
significant difference in regression slope was found (hindlimb peak vertical
force on level versus on decline; P=0.0080).

Locomotor kinetic results are summarized in
Table 3 and Figs
4 and
6, and differences in impulse
magnitudes between limbs are illustrated in
Fig. 7. Vertical impulse and
peak vertical force of forelimbs exceed those of hindlimbs during level and
decline trials (P<0.0001). Consequently, forelimbs support over
65% of the body weight when the opossums ran on the horizontal trackway and
about 82% of body weight when they ran downhill. By contrast, fore- and
hindlimbs take on nearly equal roles in body weight support during the incline
trials. Vertical forces of forelimbs are greatest on downhill trials,
intermediate on level trials, and least on uphill trials
(P<0.0001). Hindlimbs largely follow an inverse relationship: the
greatest mean values were obtained during level and uphill running and smaller
vertical forces were recorded during downhill trials (P<0.0001;
level and uphill trials did not differ significantly). On the level trackway,
peak vertical force occurred earlier in the stance phase of hindlimbs
(43.4±3.2%) than in forelimbs (58.3±3.1%; P=0.0180).
There were no significant differences in the timing of peak vertical force
between limb pairs on the sloped trackways, where peak occurred at
54.5±2.2% of stance.

Craniocaudal impulses on the horizontal trackway were typical for
terrestrial quadrupeds, in that an initial braking impulse was followed by a
propulsive impulse. Braking impulse was significantly greater in the forelimbs
than in the hindlimbs (P=0.0003), such that the forelimbs generated
nearly 78% of the total braking impulse during level locomotion. Although the
hindlimb propulsive impulses tended to be greater than those of the forelimb,
there was no significant difference between limb pairs (P=0.31). The
transition between braking and propulsive phases occurred significantly later
in the forelimbs (62.0±2.1% of stance duration) than in the hindlimbs
(33.3±3.7%; P<0.0001). On inclines, the braking impulses
were trivially small so that time of braking-to-propulsion transition was
effectively at touchdown in both limb pairs. Both fore- and hindlimbs produced
substantial propulsive impulse, approximately an order of magnitude greater
than that exerted on the level, although forelimbs provided approximately
57.7% of the total propulsive impulse (P=0.001). On declines, braking
impulse was substantial for both limb pairs, with forelimbs generating on
average 81.8% of the total braking impulse (P=0.0001). The braking
impulse generated by the forelimb on the decline trackway was the greatest of
any craniocaudal impulse recorded in this study. Fore- and hindlimbs produced
virtually no propulsive impulse on the decline, so that in almost all decline
trials there existed no effective braking-propulsion transition.

Box and whisker plots of (A) vertical, (B) braking, propulsive and (C)
mediolateral impulses. Each box represents 50% of the data, and the line
within the box represents the median. Each whisker corresponds to 25% of the
data. Asterisks represent outliers, and circles denote extreme outliers. Note
that the scale of the y axis in each plot is different. BW, body
weight; FL, forelimb; HL, hindlimb.

Mediolateral impulses of fore- and hindlimbs for level and inclined trials
were equivalent in magnitude and orientation, and they consistently indicated
a net medial substrate reaction impulse (i.e. laterally directed limb force)
for each limb. Mediolateral impulses for level trials were fairly substantial,
on the order of the craniocaudal impulses, whereas those for incline trials
were substantially smaller than the craniocaudal impulses. While medially
directed impulses were obtained for the forelimbs during downhill running, the
hindlimbs indicated net lateral impulses, so that limb pairs on the decline
exerted oppositely directed and significantly different net mediolateral
impulses (P=0.0001). Across substrates, forelimbs consistently
yielded net medial impulses that were smallest during uphill running
(P=0.0135) and approximately equal on level and downhill trials.
Hindlimbs during level and incline trials exerted equivalent net medial
impulses whereas decline trials had net lateral impulses (P<0.05
for level versus decline means).

Required coefficient of friction

The overall shape of the required coefficient of friction
(μreq) curve was largely the same across substrates or between
limb pairs (Fig. 8A):μ
req was typically highest at the beginning of the stance phase
and then fell and remained at lower values until just before lift-off when the
values rose again. Within most substrate/limb groupings, medianμ
req was uncorrelated with speed. On the level, medianμ
req of fore- and hindlimbs were statistically indistinguishable
(0.211±0.021 and 0.254±0.022, respectively) and their values
were lower than either of the two sloped substrates (P=0.0001;
Fig. 8B). Although medianμ
req was not significantly different between inclined and
declined substrates, a significant substrate–limb interaction term was
found in the two-way ANOVA (P=0.0001). When limb pairs were evaluated
separately using t-tests it was found that forelimbs had a
significantly greater median μreq than hindlimbs on inclines
(forelimb, 0.694±0.018; hindlimb, 0.478±0.028;
P=0.0002), whereas the reverse pattern existed on the declined
trackway (forelimb, 0.540±0.019; hindlimb, 0.651±0.023;
P=0.0067).

Discussion

Body weight support

Limb function during terrestrial locomotion, as reflected by SRF patterns
and limb kinematics, has best been characterized on level substrates
(Demes et al., 1994;
Schmitt and Lemelin, 2002),
and the general pattern found for M. domestica is typical of
terrestrial quadrupedal mammals. Given that body weight support is reflected
by the magnitudes of vertical SRFs or impulses, then the forelimbs of M.
domestica on level substrates support the majority of the body weight.
The most likely (and unremarkable) explanation for this is that the center of
mass of M. domestica is closer to the forelimbs than to the hindlimbs
(37% of the glenohumeral–acetabular distance). A cranially oriented
center of mass is a common feature among non-primate mammals
(Schmitt and Lemelin,
2002).

With the animal's center of mass located closer to the forelimbs than to
the hindlimbs, we expected that fore- and hindlimbs would support
approximately equal body weight on the 30° inclined substrate (Prediction
1). This was apparently the case. This finding can be explained by the
direction of the line of gravity passing through the center of mass
(G). On the incline, this gravity vector typically intersects the
substrate closer to a point roughly 50% of the glenohumeral–acetabular
distance. On the decline, the opposite occurred, and the gravity vector
G intersected the substrate more anteriorly. This explains why the
vertical impulse exerted by the forelimb was so considerably and significantly
greater on the decline. The animals were never observed to topple (pitch) over
their forelimbs, which suggests that G usually intersected the
substrate posterior to the forelimb contact on the substrate (but more
anteriorly than was the case on the level trackway).

Relative effort (%) of vertical, braking and propulsive impulses exerted by
fore- and hindlimbs. Absolute values of total impulse (forelimb + hindlimb)
are indicated to the right. Because the total propulsive impulse on the
decline was extremely low, percent limb effort was not calculated. These
percentages were calculated for illustrative purposes; because they were
calculated from the mean vertical, braking and propulsive impulses for each
substrate slope, testing for significant difference among groups was not
possible. BW, body weight.

Shear forces and the required coefficient of friction

On the level trackway, both limb pairs have braking and propulsive
components during level locomotion (Fig.
6). Thus neither fore- nor hindlimbs are exclusively responsible
for decelerating or accelerating the center of mass with every step. The
forelimbs of M. domestica are net braking whereas the hindlimbs are
net propulsive, as is typical for terrestrial quadrupeds
(Demes et al., 1994). It is
noteworthy, however, that although the forelimbs take on a larger share of
overall braking effort, forelimbs and hindlimbs share more equally the
propulsive effort, as was observed in trotting dogs
(Lee et al., 2004). This may
be due to the greater range of motion of the forelimbs in M.
domestica, although most mammals similarly have greater excursion angles
in the forelimb compared with the hindlimb
(Larson et al., 2001). A
greater limb excursion might allow that limb to apply braking or propulsive
force over a longer time within a stride. Alternatively, the opossums in the
sample may have been, on average, slightly accelerating during forelimb trials
and/or slightly decelerating during the hindlimb trials, despite our best
efforts to eliminate trials in which the opossums did not move at a steady
speed.

Frictional conditions in locomotion. (A) Typical plot of the required
coefficient of friction (μreq) in M. domestica (1.78 m
s–1) on the level trackway. Broken line represents the median
value of μreq. (B) Box plots of the median required coefficient
of friction for each substrate and limb pair. Asterisk, outlier; circle,
extreme outlier.

Rocha-Barbosa et al. suggest that the hindlimbs of guinea pigs (Cavia
porcellus) have a greater role in changing locomotor speed than the
forelimbs (Rocha-Barbosa et al., 2005). This supposition is based on the
observation that as speed increases, the hindlimb joints exhibit more
kinematic changes than forelimbs (changes in joint angles and angular
velocity). It is unknown if these differences between fore- and hindlimbs are
accompanied by kinetic differences. In our experiments on substrate effects on
opossum locomotion (this study), we observed an increased role of the
forelimbs in generating propulsive impulse on the inclined trackway. This was
an unexpected result, as we anticipated that the hindlimbs (which are
net-propulsive on the level trackway) would exert greater propulsive effort
relative to the normally net-braking forelimbs (Prediction 2). At the very
least, given that the fore- and hindlimb supported approximately equal body
weight on the incline, one might expect roughly equal propulsive impulses from
fore- and hindlimbs. Lammers and Biknevicius found that on a narrow,
horizontal, `arboreal' support, the forelimbs similarly increased their
propulsive role on the narrow trackway in comparison to the flat `terrestrial'
trackway (Lammers and Biknevicius,
2004). In M. domestica, the forelimbs may increase their
role in locomotion (as measured by craniocaudal and mediolateral substrate
reaction forces) on challenging substrates while the hindlimb function remains
relatively unchanged. It is possible that this pattern is comprehensive among
primitive quadrupedal mammals in general, but comparative force data are
needed on additional species whose body plans resemble primitive mammals.

On the inclined trackway, the forelimbs generated greater propulsive
impulse than the hindlimbs, but the role of the forelimbs in supporting body
weight decreased. These results explain the high required coefficient of
friction (μreq) observed in the forelimb on the incline, which
was the highest μreq observed in this study. Shear forces were
higher due to increased propulsive forces. Simultaneously, the normal forces
(which are largely generated by body weight, even on a 30° incline) are
decreased in the forelimbs. With greater shear and lower normal forces, theμ
req of the forelimbs is significantly greater on the
incline.

Whereas fore- and hindlimbs had equivalently low median μreq
on the level substrate, the median μreq is significantly higher
in both limb pairs on both inclined and declined trackways. The substrate
slope apparently causes the body weight to increase the shear forces and
contribute less to normal forces. This is consistent with data on humans
walking on gradients (McVay and Redfern,
1994), but there are no comparable data for animals roughly the
size of M. domestica. Despite the increase in μreq on
the sloped terrain, the animals never slipped in any of the trials used for
this study, and rarely slipped during any trial. This is because theμ
req is lower than the true coefficient of friction
(μs), which was not measured. Two other studies provide
estimations of μs: Kinoshita et al. calculated μs
between 220-grit sandpaper and human skin (thumb and index finger) to be above
1.5 (Kinoshita et al., 1997),
and Cartmill estimated μs between the volar skin of primates and
a plastic surface to be above 5 (Cartmill,
1979). Both of these values are substantially greater than the
median μreq computed for M. domestica on the
sandpaper-covered trackways (maximum value=0.96). The animals' claws must also
provide additional traction on the level and inclined trackways.

Mediolateral forces control yaw and provide some stability against rolling.
Mediolateral impulses were medially directed in M. domestica,
reflecting of laterally directed limb forces. The most striking feature of the
mediolateral impulses is their magnitude: mediolateral impulses are nearly
equivalent to craniocaudal impulses. The likely explanation for relatively
high mediolateral impulses is that M. domestica maintains a
moderately abducted limb as commonly found in non-cursorial mammals
(Jenkins, Jr, 1971). By
contrast, many terrestrial mammals, and especially those that are cursorial,
have mediolateral forces that are so negligible that they are customarily
ignored (e.g. Bertram et al.,
2000). The mediolateral impulses of M. domestica are
greater in comparison to mammals with erect limb posture, but low relative to
tetrapods with more sprawled limb postures such as lizards
(Christian, 1995) and
alligators (Willey et al.,
2004). Indeed, M. domestica maintains a moderately
abducted limb, as commonly found in non-cursorial mammals
(Jenkins, Jr, 1971). We
conclude that high mediolateral forces may be a hallmark of tetrapods that
move in non-parasagittal locomotion.

On both inclined and declined trackways, we predicted that the mediolateral
impulses would not differ greatly from those observed on the level trackway
(Prediction 4). This was not the case. On the inclined trackway, net
mediolateral substrate reaction impulses remained medially directed, as they
were on the level trackway. But they were about 19.8 times smaller in the
forelimb, and about 3.6 times lesser in the hindlimb relative to their
magnitude on the level. Thus, a greater amount of muscular effort was devoted
to toward propulsion, and away from stability and ability to change direction.
This is especially true in the forelimb, which had greater propulsive effort
than the hindlimb, but less mediolateral effort. Substantial medially directed
reaction impulses were commonly observed in the forelimbs during decline
locomotion in M. domestica. Although the forelimbs tend to be
somewhat more abducted on decline trials, they are not significantly more
abducted than they were on the level or incline substrates. But the hindlimbs
undergo considerable adduction during stance on all substrates, suggesting
lateral undulation of the spine (Pridmore,
1992). This apparent lateral undulation is somewhat (but not
significantly) greater on the decline, and this may partially explain the
larger lateral forelimb forces. Also, the hindlimbs exerted laterally directed
net mediolateral impulses, which is the opposite direction of the forelimb net
mediolateral impulse. But because these animals use primarily trotting gaits
regardless of substrate slope (this study,
Fig. 3), a medial SRF in the
forelimb and a lateral SRF in the contralateral hindlimb have the effect of
pushing the animal to one side or another. These mediolateral forces should
cause the animal to move from side to side (right and left) as it moves
downhill, which may serve to control the rate of descent.

Limb kinematics

Our results indicate that shoulder height is always lower than hip height,
but we believe that shoulder and hip heights in M. domestica are
probably more similar than our data indicate. This is because we measured the
approximate location of the glenohumeral joint as the pivot point of the
shoulder rather than the middle of the scapula
(Fischer et al., 2002).
Measuring the scapula was impossible using videography, but despite the lack
of data on shoulder blade excursion, we believe our results comparing
substrate effects on forelimb excursion are valid. Total forelimb angles were
measured in the same way regardless of substrate, which means that relative
differences among substrates are most likely real differences.

Our predictions of how limb protraction at touchdown, limb retraction at
lift-off, and overall limb posture would change with substrate slope were
based on the assumption that the locomotor behavior of the animals would
maximize stability (Predictions 5 and 6). This was partially borne out. M.
domestica assumes a high degree of crouching, with its forelimbs during
incline locomotion, and hindlimbs during decline locomotion. These kinematic
adjustments brought the center of mass somewhat closer the substrate, which
causes G to remain closer to the center of the base of support. These
adjustments to limb posture also had the effect of leveling the animal's body,
a behavior commonly reported among primates moving on inclined and declined
substrates (Vilensky et al.,
1994; Stevens,
2000; Krakauer et al.,
2002). Similar increased hindlimb crouching during substrate
descent was reported for squirrel monkeys
(Vilensky et al., 1994) and
desert iguanas (Higham and Jayne,
2004). Because M. domestica did not crouch with the limb
pair located lower on the trackway (hindlimbs on the incline, and forelimbs on
the decline; see Fig. 4) the
opossums maintained a relatively lower rotational moment about the
hip/shoulder, thereby reducing the likelihood of toppling over the downslope
limb pair.

As is the case with most mammals
(Larson et al., 2001), the
forelimbs of M. domestica undergo greater craniocaudal excursion than
the hindlimbs. Although the amount of limb protraction and retraction differed
on inclines and declines, this difference between forelimbs and hindlimbs was
consistent.

We predicted that on the incline, both limb pairs would undergo greater
retraction, especially at touchdown, in an effort to keep G located
within the base of support (Prediction 6). On the decline, both limb pairs
should protract more, especially at touchdown. The limbs did not behave as
predicted on the incline; this, in addition to the net mediolateral impulse
results, suggests that 30° incline locomotion does not destabilize the
opossums as much as decline locomotion. On the decline, both limb pairs were
more protracted at touchdown, which will keep G located within the base
of support. Furthermore, with the limbs more aligned with the gravity vector,
the rotational moment about the shoulder may decrease. In summary, the
relatively extreme kinematic adjustments, the considerable loading on the
forelimbs, and the claws (which most likely are less effective on the decline)
strongly suggest that moving downslope is more challenging than moving
uphill.

In spite of changes in limb function during locomotion on the sloped
trackways, the shoulder and hip movements (perpendicular to the surface of the
trackway) of M. domestica continued to exhibit the `bouncing' pattern
similar to that described on the level trackway. This pattern suggests that
the animals are running, e.g. converting gravitational potential energy and
kinetic energy into stored elastic strain energy in their tendons during
midstance (Cavagna et al.,
1977). As with level locomotion, the storage and utilization of
elastic energy during incline/decline locomotion may be limited in mammals as
small as M. domestica (Ettema,
1996; Biewener and Roberts,
2000). Furthermore, recovery of external mechanical energy may not
be universal on inclined substrates: whereas peak stresses measured from the
tendons of leg muscles of guinea fowl moving on level and incline trackways
suggest that elastic energy storage increases on inclines
(Daley and Biewener, 2003),
they are unchanged in the tammar wallaby
(Biewener et al., 2004), so
that enhanced recovery of external mechanical energy when running on inclined
substrate is not universal.

Conclusion

Some of our results are explained by body weight support. The craniocaudal
location of the center of mass accounted for the differences in relative
magnitudes of vertical forces between fore- and hindlimbs and among
substrates. Body weight support also seems to explain why the forelimbs
exerted a much greater braking impulse than hindlimbs while descending a
30° decline. Second, the need to remain stable during locomotion appears
to account for mediolateral impulses and the required coefficient of friction
results, as well as limb excursion of shoulder/hip heights. However,
craniocaudal impulses on the inclined trackway could not be explained by
either body weight support or stability. There is also no outstanding
morphological feature that gives a reason for this phenomenon: fore- and
hindlimbs are approximately the same size, and they have the same number of
digits (five). Also, all the digits (except the hallux) have claws. The
craniocaudal impulses measured during incline locomotion imply that the
locomotor behavior of forelimbs may be more malleable than hindlimbs, and that
when an animal encounters a challenging substrate, its forelimbs might modify
their locomotor behavior more than the hindlimbs
(Lammers and Biknevicius,
2004).

List of symbols and abbreviations

COM

center of mass

FCC

craniocaudal force

FDV

dorsoventral force

FML

mediolateral force

FV

vertical force

G

gravity vector through COM

l

distance between knife edges of reaction board

Rs

amount of weight supported by the reaction board knife edge over the
weighing scale

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